Vector Calculus Questions and Answers

Mathematics is not about numbers equations computations or algorithms it is about understanding 5 5 pts 6 6 275 Sketch the region bounded by y x and y 5 Compute the center of mass of the region 6 4 2 On t 2 2 4 4 a William Paul Thurston American mathematician X

Evaluate the line integral de by evaluating the surface integral in Stokes Theorem with an appropriate choice dr G of S Assume that C has a counterclockwise orientation when viewed from above C is the circle x y 29 in the plane z 0 Rewrite the given line integral as a surface integral F ff dS TAX

1 Find a unit vector u such that Duf Po 0 for f x y 3 sin ry 2 7e4y and Po 3 0

The percentage of the population of a city infected t days after seasonal flu arrives is given by p t 13e for 0 t 30 After how many days is the percentage of infected people at a maximum Round your answer to the nearest whole number

Does the intermediate Value Theorem guarantee that the following function has a real zero between 1 and 2 g x 6x 246x 210x 618x 252 Answer 2 Points

A box company makes a variety of boxes all with volume given by the formula x 12x 45x 50 If the height is given by x 5 what is the formula for the area of the base 1 Keyp

2 0 5 0 6 5 pts Openstax 6 4 207 The base of a lamp is constructed by revolving a quarter circle y 2x x around the y axis from x 1 to x 2 Develop an integral for the surface area of this curve and compute it 2 y 2x 2 1 OX 0 1 2

2 f x 8 6 2x 4 2 x 2x 3 Ay 2 4 2 2 4 6 X

In AVWX v 47 cm w 11 cm and x 38 cm Find the measure of ZW to the nearest 10th of a degree Law of Cosines SSS May 07 6 20 20 PM Watch help video

3 f x 2 100 8 3x 3 x 4 6 2 Ay 8 6 2 2 6

Admission to a baseball game is 4 00 for general admission and 5 50 for reserved seats The receipts were 5973 50 for 1358 paid admissions How many of each ticket were sold Round to nearest integer if necessary Answer How to enter your answer opens in new window general admission tickets sold Keypad Keyboard Shortcuts

Select the graph for each system of inequalities below 4x 4y28 2x ys l 16 70 yzx 70 3x 3y 9 17 T

For each transformed function g x find the following a g x 2 3 x 4 1 2 b g x 5 7 x i Parent function f x ii Mapping notation iii Transformation table with three points iv Sketch of g x using the transformation table v Domain of g x v Range of g x 1 KU 1 KU 1 5 A 3 C 0 5 A

In AGHI h 820 inches mZG 102 and m H 10 Find the length of g to the nearest inch

What is the coefficient of the term containing x y in the expansion of 5x y AnswerHow to enter you

rplane travels at an average velocity of 618 kilometers per hour for 2 hours and 30 minutes How he airplane travel ance traveled by the airplane is I kilometers

Convert the radian measure to degrees 11x 9 11T rodiens

Convert the angle in degrees to radians Express your answer as a multiple of 95 95 radians Type an exact answer using it as needed

Question 12 Use Graphical Calculator to find all zeros for g x x 6x 1 O x 0 16 x 2 36 O x 0 16 x 2 36 O x 0 16 x 2 36 O x 0 16 x 2 36

Find all zeros of the function f x 2x 18x 52x 48 Enter the zeros separated by commas

Solve the given equation for x 52x6 32 X Basic Funcs Trig

Find all zeros of the function f x 4x 12x 100x 300 Enter the zeros separated by commas Question Help Video Submit Question

Three pens of the same size are to be built along an existing fence If 320 feet of fencing is available what length should x and y be to produce the maximum total area What is the maximum area x feet X www y X

Give a verbal description of the region R and determine whether R is a regular x region a regular y region both or neither R x y x 6 ly 7 Choose the best description of the region R below O A R is a rectangle with vertices 7 6 7 6 7 6 and 7 6 B R is a rectangle with vertices 6 7 6 7 6 7 and 6 7 OC R is a circle with radius 7 OD R is a circle with radius 6 Determine whether R is a regular x region a regular y region both or neither O A R is a regular x region OB R is neither a regular x region nor a regular y region OC R is a regular y region OD R is both a regular x region and a regular y region

Show that f n 13 23 n is O n4 For the t

3 Use the 8 rectangles shown to approximate the area of the region below the graph of f x 10 x over the interval 1 3 1 1 2 3

The equation for the elastic displacement of a beam is y x c x 8 3 x x Perform one iteration of Newton s method for finding its maximum point of y x by starting from x 1 OA Unknown due to the value of c OB 0 5 OC 0 3333 D 1 5 E 0 6667

8 10 points Use Newton s method with the specified initial approximation xi to find x3 the third approximation to the root of the given equation Round your answer to four decimal places r5 x 7 0 x l

2 An engineering student was given an assignment to construct a triangular model of the three steel girder Two of the girders measured 20cm and 15cm and the angle opposite the 15cm girder was 21 How lon does the third girder have to be

5 5 Calculate XYk for the n 5 data points x 0 4 x2 2 2 5 x3 Y3 4 8 x4 Y4 6 10 and 5 k 1 k 1 x5 5 8 14 5 xk YK Simplify your answer

Find the average rate of change of g x Question Help Video 3x 4 from x 4 to x 2

13 83 Mark s morning class scored an average of 89 25 points across 4 tests His evening class scored an average of 94 50 points across 4 tests What was the average test score between both classes across all 8 tests Estimate your answer to 2 decimal places

A culture of yeast grows at a rate proportional to its size If the initial population is 8000 cells and it doubles after 4 hours answer the following questions 1 Write an expression for the number of yeast cells after t hours Answer P t 2 Find the number of yeast cells after 5 hours Answer 3 Find the rate at which the population of yeast cells is increasing at 5 hours Answer in cells per hour

Match each equation with its graph 12 10 8 6 4 2 X 4 6 y 12x x 8y x 2y x 1 4 x 3 A T cy 7 4 U t 10 3 7 2 cy B 5 4 y 3 2 7 O 4 X

13 If a point is placed at random on AE below find each probability as a fraction in simplest form 0 B 12 a P on AC b P not on BD 30 C 27 D30 24 36 E 48 7 16 14 A shuttle bus arrives at a hotel every 40 minutes to take guests into town If a guest walks out the door at a random time find the probability of each waiting time a P at least 15 min b P no more than 10 min

Points z and Z2 are shown on the graph 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 1 2 3 5 6 7 8 9 Imaginary Axis Z1 12 3 4 Real axis 5 6 7 8 9 22 Part A Identify the points in standard form and find the distance between them Part B Give the complex conjugate of z2 and explain how to find it geometrically

Use the vectors in the figure at the right to graph the following vector 3v u 3w Select the figure with a vector that is equivalent to 3v u 3w A 1 Q B fra O C D

Three point masses with masses of m 4 m 2 and m3 are located respectively at points 6 P 8 8 P2 0 4 and P3 2 7 The center of mass for this system is located at x y

se synthetic division to rewrite the following fraction in the form g x r x d x mainder where d x is the denominator of the original fraction q x is the quotient and r x is 4x 15ix 3x 5 4 x 31

They request you find the volume of the solid that is built with the interior of a sphere x2 y2 z2 2z y above the paraboloid z x2 y2 using polar coordinates what would be the volume comprised

plot that is as a function of time n Upload a picture of your graph 4 Predator Prey Population Model in the wild the population of a predator species such as foxes depends on prey species such as rabbits so the populations are interrelated un rabbit population at time n un 1 1 a b v 1 v fox population at time n v 1 1 c un 1 d where a growth rate of rabbit population where there are no foxes 0 047 b rate at which foxes kill rabbits 0 0011 c growth rate of fox population when there are rabbits 0 00019 d death rate of foxes when there are no rabbits 0 032 Let the initial conditions be uo 288 rabbits and vo 63 foxes a Graph the sequences un and v as functions of time n on the same set of axes Upload a picture of your graph

Find a formula for the inverse of the following function if possible Answer How to enter your answer opens in new window A x 2x 4 Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is A x does not have an inverse function

Consider the following function 3 cos x f x What conclusions can be made about the series n 1 3 os n n and the Integral Test 4 The Integral Test can be used to determine whether the series is convergent since the function is positive and decreasing on 1 co The Integral Test can be used to determine whether the series is convergent since the function is not positive and not decreasing on 1 co O The Integral Test can be used to determine whether the series is convergent since it does not matter if the function is positive or decreasing on O The Integral Test cannot be used to determine whether the series is convergent since the function is not positive and not decreasing on 1 co O There is not enough information to determine whether or not the Integral Test can be used or not

Find the component form of the vector v 300 O 88 152 42 56 56 67 41 O 0 5 0 866 44 76 21 Y 88 X

Find the component form of the indicated vector Let u 2 7 v 6 5 Find v u 9 1 8 2 3 13 4 12

Find the unit vector in the direction of the given vector Write your answer in the indicated form Let u 1 3 Find the unit vector in the direction of u and write your answer as a linear combination of the standard unit vectors i and j Oi j 00 0 Oi j 0

Prove that RS and OP are equivalent by showing that they represent the same vector R 3 3 S 12 4 O 0 0 and P 9 1 Yes No

Given the matrices A and B shown below find A B A E 0 6 3 0 12 12 6 0 9 Rows 2 Columns 2 B 11 11 4 4 10 1 12 7

Select the answer for each question below 70 The solution set of 4x 8y 16 lies in which quadrants A II only D II III and IV B I and III E I III and IV C I II and III

Given the matrices A and B shown below find B A Rows 2 A 3 15 18 6 18 15 9 0 B Columns 2 10 10 1 3 3 11 6 11